Edit: The article doesn't even mention any rep from SpaceX saying they're profitable. This SEEMS like a guesstimate by the writer
The existence of various ways of considering the finances of a corporation don't necessarily mean that any one method is "wrong". But when you get into questions of "is it profitable?" The answer depends a lot on who's asking.
In any one month, more money may go out of your checking account than came in, but does that mean you lost money that month? Maybe some of the outgoing money was paying for a year's worth of an expensive service, or was an investment in some other company, or was the purchase of some assets that will allow you to become more productive. In those cases, while your cash flow may be negative, you can keep a set of books that spreads the cost of a year's worth of service over the entire year, even if you pay it all at once on January 1. Or a building you might want to spread the cost out over the duration of any loans you took out to pay for part of it, or if you paid cash, you still may want to spread the expense out over the 15 year expected lifetime of the asset.
Obviously the IRS and SEC rules have to be pretty standard across the board, but within any particular industry or business model, a different representation may provide investors or management with a more accurate picture than the IRS or SEC rules would allow.
Obviously all of these can be abused, and investors should be skeptical and do due diligence, but even 100% honest businesses may report a loss to the IRS, a profit to investors, and a break-even for the SEC. They aren't necessarily trying to scam anyone.
Pretty much everything you mention in this paragraph is covered by accounting rules a student would learn in year 1. Cash flow isn't profitability. Spending on assets is capitalized, and they depreciate according to rules, not what you "may want" to do.
Yes, there is always some leeway to play fast and loose with accounting, and companies are always trying "adjust" earnings to suit to their business model. 4 times out of 5, it's horsecrap. That's why we have GAAP.